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Archiv der Mathematik

, Volume 92, Issue 1, pp 57–69 | Cite as

Inverse positivity for general Robin problems on Lipschitz domains

  • Daniel Daners
Article

Abstract.

It is proved that elliptic boundary value problems in divergence form can be written in many equivalent forms. This is used to prove regularity properties and maximum principles for problems with Robin boundary conditions with negative or indefinite boundary coefficient on Lipschitz domains by rewriting them as a problem with positive coefficient. It is also shown that such methods cannot be applied to domains with an outward pointing cusp. Applications to the regularity of the harmonic Steklov eigenfunctions on Lipschitz domains are given.

Mathematics Subject Classification (2000).

35J25 35B50 35B65 

Keywords.

Elliptic boundary value problems Robin problems Lp-estimates maximum priciple Steklov eigenfunctions 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsThe University of SydneySydneyAustralia

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